First, test strips are highly unreliable so I would never trust the numbers they are giving you.
As to the specific question, understand that TA really only affects how fast pH rises in our pools. We have found through the tens of thousands of pools our members own that with TA100+ you end up with pH that goes up too fast and you need to keep adding acid to keep it in check.
I bought a house with a 23,000 gallon in ground gunite (concrete) pool and had no idea how to take care of it. We find that many times people turn to friends/relatives with a pool or the local pool store to "learn" how to take care of it. The friends/relatives generally can tell you how they take care of those, but generally don't have a depth of knowledge to say why what they do works or maybe doesn't work. Again, like yourselves many people show up here thinking that an outbreak of algae once or twice a year is "normal" and that you drain and refill your pool evey couple of years because the water gets "stale". I'm here to tell you , both ar false.
First, pool store employees primary goal is to sell stuff, not necessarily get your pool in perfect condition. As to whether that is because of improper training, lack of knowledge or just to sell stuff I will leave up to you. While you would think that a "professional" would be the best, unfortunately in most cases it is quite the opposite. Between employees who blindly trust the word of chemical sales representatives and high school kids working in the pool store for the summer you end up with poor results from their advice and testing. The pool store want's you to have "a shed filled with white bottles of pool chemicals that had mysterious names and purposes". Unfortunately the pool industry has evolved into sales by scare tactics, misdirection, misinformation and marketing hype. Go in to the store and tell them your Total Alkalinity (TA) is low and they are going to sell you baking soda in a fancy package at four times the cost of WalMart. Do they have a right to make a profit, yes - but lets be reasonable. Heck, even their definition of "low" can many times put you on a pH roller coaster that's hard to get off of. Is that lack of knowledge or a sales technique to sell you more chemicals to control your pH????
What do we propose? We base our pool care system on accurate testing and only adding what the pool needs, when it needs it. Which leads to
TFPC tenet - Never put chemistry in your pool when you do not know the outcome
For almost everything the pool store sells, there is a generic "twin" that you can get at your grocery store or big box store. Alkalinity low like I used as an example? You can go to the pool store and buy Alkalinity Up in a fancy bottle or you can stop by Walmart and pick up baking soda.
So, to control your pool you need to know what is going on. Many folks have a Saturday morning ritual, dip a bottle of water out of the pool and take it to the pool store (they give you the bottle for free). They test it and sell you what they say you need to "fix" what ails your pool. But, you will find not much credence is given to pool store testing around here. While you would think that a "professional" would be the best, unfortunately in most cases it is quite the opposite. Plus, the results of their "testing" is used to convince you that you need to buy things. Why do you think that testing is free?
But, what can you do?? You need your own accurate test kit! Order a TF-100 Test Kit ™.
Pool stores sell a lot of trichlor pucks to chlorinate and they are very acidic. Keeping a high TA prevents the pH from crashing and dissolving the heater and the plaster when using them. Check out the pictures Maintain your chemicals correctly